Its PERSONAL because it will separate spouses and children, end careers etc. Its not an "agree to disagree" situation if your nearest and dearest express disregard or even contempt for you and your spouce, children, career and life plans
In all the apocalyptic prophecies about Brexit, I have heard nobody suggest that it would split marriages and end careers. Nor can I imagine people's 'nearest and dearest' disregarding or showing contempt for their parents over Brexit, if that disregard and contempt wasn't already present, though hidden.
DDiL and I recently found ourselves on either side on another very contentious issue, with DDiL being very emotional about it. Immediately I realised this I stopped the conversation and we gave each other a big hug and agreed we would put the issue to one side as both of us felt so strongly on the issue that discussion would be pointless, neither would convince the other to change. We both respect each others views even if we do not agree. That is how most families work.
On Brexit, there is no argument. We all voted Remain, but even here DD considered long and hard about it and was, for some time going to vote for Brexit, although she did not in the end, none of us did anything to persuade her, we respected her real doubts about the EU, although we were glad when she did decide to support Remain.